Conventional sheet making machinery for producing a continuous web or sheet of material includes equipment to set the sheet properties of the web as it is being manufactured. Generally, on-line measurements of sheet properties are made by scanning sensors that travel back and forth across the width of the sheet of material in the cross-machine direction (CD). The machine direction (MD) is the direction of travel of sheet. The scanning sensors are located downstream of actuators that are controlled to adjust the sheet properties. The scanning sensors collect information about the sheet properties to develop a property profile across the sheet and provide control signals to the appropriate actuators to adjust the profile toward a desired target profile in a feedback loop. In practice, the actuators provide generally independent adjustment at adjacent cross-directional locations of the sheet, normally referred to as slices.
High performance cross-directional (CD) control of sheet making machines, particularly, paper machines, requires accurate knowledge of the controlled process model. Particularly important for CD control is an accurate knowledge of the mapping between CD actuators and their response centre positions in the measurement scan. Mapping involves establishing the relationship between each downstream slice where scanning measurements occur and the corresponding upstream actuator that must be adjusted to control the particular downstream slice. In practice, this mapping depends on the paper alignment and shrinkage which varies from one paper machine to another and with time for the same machine.
Alignment
The general problem of the CD response identification can be subdivided into the problems of identifying shapes of the actuator responses and determining alignment. The alignment problem could be considered as a problem of determining a distribution of the actuator response centres.
In the paper making industry, the distribution of the actuator response centres is jointly defined by the following factors:
1. Geometrical alignment of the CD actuators and scanner. PA1 2. Position of the individual actuators within the CD actuator array. PA1 3. Wandering of the paper web. PA1 4. Paper shrinkage characteristics. PA1 1. The system should provide for a reliable automated identification of the paper alignment and shrinkage parameters, based on the results of specially designed bump tests. PA1 2. The system should be able to work for an actuator excitation pattern of a general type that is not limited to the typical bump test pattern. This would make it possible to extend the approach for on-line use. PA1 3. The alignment identification should be insensitive, robust to the mismatch of the bump response model. PA1 4. The identification should be reliable despite a possible high level noise in the data. PA1 5. The identification should require data for a small number of the scans, ideally 10 to 20. This would speed up the data collection process and reduce the amount of the product scrapped as a result of the identification tests. PA1 6. Two versions of the algorithm need to be developed. The first, simpler version, should be applicable in the case of a linear (uniform) shrinkage. Based on practical experience, such simpler version of the alignment algorithm is sufficient in 80-90% of all cases. The second, more advanced version should allow for the identification of a nonlinear shrinkage profile. PA1 7. The shrinkage profile should be determined as a smooth function of the CD coordinate: any rapid variation of the shrinkage in the CD is likely caused by the identification error. PA1 8. The shrinkage identification should be maximally automated and easy to use. It should require as little operator input as possible.
The first two items could be, in principle, determined from an accurate measurement of geometrical parameters of a paper machine. The last two, however, can change with the time and different paper grade and need to be experimentally identified in each case. The paper web wandering can be determined by using additional sensors and monitoring the physical edges of the sheet at the actuator and scanner locations. On the other hand, the paper shrinkage is a complicated phenomenon depending on the paper furnish, drying process and many other factors.
A conventional method for measurement of the paper shrinkage is to do a dye test, by inserting dye into the paper at the actuators and recording where the dye falls at the scanner. Dye tests are very lengthy and tiresome procedures requiring considerable manual labor.
The most suitable technique is believed to be identification of the alignment by exciting actuators (input) and observing experimental response (output). Such an input/output approach by design identifies a final result of the joint action of all factors influencing the alignment. The input/output identification technique is the most adequate for the subsequent CD controller design, since the same type of data (high resolution profile) is used for determining alignment as the data used to evaluate performance of the operating control system and to design CD control strategies. Another advantage of the input/output identification of the alignment is that it can be automated with a control computer which alleviates the need for the operator intervention, and facilitates a more regular tuning of the control system.
An approach to the input/output identification of the alignment which is commonly used in practice is to perform "actuator bump tests" by disturbing selected actuators and detecting their response by averaging many scans of the paper properties. The response centres can be then determined through the maximal response amplitudes. Knowledge of the response centre distribution allows one to determine the average shrinkages between the bumped actuators. However, the described traditional approach has a few deficiencies, the most serious of them being an unacceptable poorer paper quality produced as a result of each session, lack of reliability, and poor noise rejection.
Shrinkage
In many cases, the paper shrinkage is linear, i.e. uniform across the sheet. In that case, a combined effect of the shrinkage and alignment factors is defined by just two parameters of an affine transformation between the actuator number and the response centre position.
Theoretically, for a general nonlinear nonuniform shrinkage, a position of each response centre should be defined individually. This would require using as many parameters as there are actuators.
Practically, the paper shrinkage is defined by a shrinkage profile which is a smooth function. Most of the shrinkage appears in the dryer section. Typically, nonuniform shrinkage is caused by the nonuniform restraint of the paper in the dryer felts. The restraint is weaker at the edges, hence, the shrinkage is higher at the edges. Generally, shrinkage is roughly constant in the middle of the paper sheet and increases at the edges. Variations of shrinkage in the middle appear to be caused by shrinkage measurement error. Therefore, the algorithm developed for the process of this invention is based on the assumption that the shrinkage profile has a standard shape. The shrinkage is assumed to be constant in the middle and growing at the edges. The edge shrinkage is described by the edge zone width and the maximal shrinkage at the edge.
Based on the above discussion, an advanced shrinkage identification system should satisfy the following requirements: